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6.43125n^2-22.5n+15=0
a = 6.43125; b = -22.5; c = +15;
Δ = b2-4ac
Δ = -22.52-4·6.43125·15
Δ = 120.375
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22.5)-\sqrt{120.375}}{2*6.43125}=\frac{22.5-\sqrt{120.375}}{12.8625} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.5)+\sqrt{120.375}}{2*6.43125}=\frac{22.5+\sqrt{120.375}}{12.8625} $
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